GRAND RAPIDS, Minn. — For 70 of the past 72 years, a Democrat has represented this rural corner of northern Minnesota in Congress. But when loggers, foresters and truckers convened on the county fairgrounds here for the annual timber industry expo last month, the star of the “celebrity log-loading” contest was a Republican.

He is Pete Stauber, a former professional hockey player and retired police lieutenant with a ramrod-straight bearing and a politician’s firm grip. He may also be his party’s best hope for pulling off this year’s most improbable feat: flipping a Democratic House seat.

As Republicans brace for a “blue wave” that could cost them control of Congress, they can count on one hand their opportunities to play offense. Mr. Stauber’s race — in a union-heavy, Trump-friendly, mostly white working-class district that includes the mining region known as the Iron Range — is their best shot.

And in Mr. Stauber, Republicans have a candidate from central casting.

“This race is the No. 1 pickup for Republicans in the entire country,” Mr. Stauber, 52, boasted after he took his turn in the log-loading contest, which consisted of climbing aboard a huge orange rig and carefully maneuvering its claw to stack one thick slice of tree trunk, painted with the face of Paul Bunyan, over another.

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The annual timber industry expo in Grand Rapids, Minn., last month.CreditTim Gruber for The New York Times

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Logs painted to look like Paul Bunyan during a contest at the expo.CreditTim Gruber for The New York Times

In all, four of Minnesota’s eight House seats are in play next month. The retirements of two Democrats in districts that President Trump won — Representatives Rick Nolan and Tim Walz — have created openings for Mr. Stauber and another Republican, Jim Hagedorn, a perennial candidate who narrowly lost to Mr. Walz in 2016. And Republicans are defending two vulnerable incumbents — Representatives Jason Lewis and Erik Paulsen — in the Minneapolis suburbs, making traditionally blue Minnesota a critical battleground.

“The bellwether for this cycle is Minnesota,” Representative Steve Stivers of Ohio, the chairman of the National Republican Congressional Committee, told reporters in Washington recently, adding, “If we lose both the incumbent races and win none of the challenger races, we’re probably in the minority.”

No battleground district in America had as big a swing from Barack Obama to Mr. Trump as this one, Minnesota’s Eighth, which includes heavily Democratic Duluth and stretches north, through the rugged Iron Range, to the Boundary Waters wilderness at the Canadian border. Mr. Obama won it by six percentage points in 2012; Mr. Trump won it by 16 points in 2016.

“The popularity of President Trump in Minnesota’s Eighth Congressional District is as intense, if not more, than on election night,” Mr. Stauber declared in an interview, as he prepared to march in the annual Hoghead Parade in the city of Proctor. “He’s fighting for our way of life, mining, manufacturing timber harvesting, low unemployment.”

Proctor, in the eastern part of the district just outside Duluth, is Democratic union turf. Its little downtown is pockmarked by vacant storefronts and overshadowed by a vast railroad yard — a remnant of the days when the Iron Range mines and the city itself, founded as a transport hub for iron ore, were booming.

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Mr. Stauber stood for the pledge of allegiance at a Republican dinner. CreditTim Gruber for The New York Times

But the Stauber name is well known in the area; Mr. Stauber is a commissioner in the county that includes Proctor and Duluth, and he has a sprawling extended family. His brief career with a minor league affiliate of the Detroit Red Wings gives him a certain cachet in hockey-crazy Minnesota. And it does not hurt that his younger brother, Robb, coached the 2018 women’s Olympic hockey team to a gold medal.

“He has a good pedigree,” said Jake Benson, 66, the publisher of The Proctor Journal, who went to school with two of Mr. Stauber’s cousins. “If you were trying to cast a candidate, he’d be it. And when it comes to things the president says, he’s smart enough to keep his mouth shut.”

As he courts the working-class men and women — many of them Democrats — who went big for Mr. Trump, Mr. Stauber is creating a mix-and-match playbook. He embraces the president, who campaigned for him at a rally in Duluth in June, and is a vocal opponent of abortion and a fervent backer of gun rights. But he also casts himself as a “blue-collar conservative” and “union Republican,” reminding voters that he once served as president of the union representing Duluth police officers.

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President Trump won Minnesota’s Eighth District by 16 points in 2016.CreditTim Gruber for The New York Times

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Mr. Stauber embraces Mr. Trump but has also cast himself as a “union Republican.”CreditTim Gruber for The New York Times

With his look-you-in-the-eye gaze and close-cropped military-style haircut, Mr. Stauber looks every bit the law enforcement officer he once was. He is playing up his image as a law-and-order family man. His wife, Jodi, an Air National Guard veteran, and four children, including a 16-year-old with Down syndrome, joined him on the Hoghead Parade float.

Rather than ride, Mr. Stauber speed-walked the parade, determined to shake as many hands as possible. The district’s shifting alliances were clear; many parade-goers sported both Stauber stickers and Klobuchar stickers, for Senator Amy Klobuchar, a Democrat standing for re-election in November.

“I like his platform; I like his personality,” said Dick Kieren, 76, a retired schoolteacher who will vote for Mr. Stauber. But he will vote for Ms. Klobuchar too: “I could never leave Amy.”

But Paula Peterson, 61 and a former Duluth city employee — “I actually worked for Mr. Stauber,” she said — was skeptical. “This is the heartland of the Democrats,” she declared.

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Joe Radinovich, Mr. Stauber’s Democratic challenger, at a parade in Chisago City, Minn. The two agree on at least one thing: Mr. Trump’s steel tariffs.CreditTim Gruber for The New York Times

Still, Mr. Stauber seems to be gaining ground. The race had been considered a tossup until this week, when David Wasserman, who analyzes House races for the Cook Political Report, moved it to “lean Republican.”

Republicans in Washington are making the race a top priority. Mr. Trump has raised money for Mr. Stauber, and Vice President Mike Pence headlined a fund-raiser for him in August. Outside groups — Republican and Democratic — have already spent more than $7 million on the seat. Nearly $6 million of that has gone to attack ads against Mr. Stauber’s opponent, Joe Radinovich, a 32-year-old former state legislator who has lined up more than a dozen union endorsements, including the United Steelworkers and the Iron Workers Local 512, which represents Minnesota.

The two candidates are philosophical opposites, with one exception: Both men support Mr. Trump’s steel tariffs, which are viewed as an economic lifeline for this region.

The race is exposing a rift among Minnesota Democrats — known here as the Democratic Farmer Labor Party, or D.F.L. — that could hurt Mr. Radinovich. Progressives and environmentalists in the Twin Cities are at odds with farmers and miners, many of whom feel the D.F.L. has left them behind. Mr. Stauber, hoping to exploit those divisions, has lined up support from the mayors of five cities in the historically Democratic Iron Range.

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Minnesota’s Eighth District has been a Democratic stronghold.CreditTim Gruber for The New York Times

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At the parade in Chisago City.CreditTim Gruber for The New York Times

“The Democratic Party has rejected us,” complained one of those mayors, Larry Cuffe Jr., of the city of Virginia. Mr. Cuffe, a lifelong Democrat, backed Mr. Trump in 2016 and will vote for Mr. Stauber — a stance that, he says, brought him “some pretty nasty emails about being a traitor to the Democratic Party.”

Here in Grand Rapids, a little city of about 11,000 surrounded by forest at the western edge of the Mesabi Iron Range, Mr. Stauber arrived at the timber expo dressed in a blue golf shirt with his campaign logo, tan pants and — in case anyone doubted his allegiance to Mr. Trump — a black ball cap emblazoned with the phrase “Make Logging Great Again” in gold letters.

“Just look at that hat,” said Kyle Ledin, a 25-year-old logger who grew up in a family of Democrats, explaining why Mr. Stauber would have his vote.

As the candidate made his way around the fairgrounds, past the Moose Lodge and the Corn Palace — “Shuck for a Buck!” the sign said — he moved easily through the crowd, demonstrating the politician’s art of making connections at every turn. His brother coached one man’s son in hockey. A woman whose grandson has Down syndrome asked his advice; he pulled out his phone to show her a picture of his son. A lumber company owner knew someone in his family.

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The Carlton County Fair in Barnum, Minn., in August. Progressives and environmentalists in the Twin Cities are at odds with farmers and miners. CreditTim Gruber for The New York Times

He sidled up to one woman, Sheila Lund, 48, a credit union loan officer, and whispered that he liked her shirt, which read “Jesus Saves.” She spun around, startled, and he introduced himself.

“Nice to meet you! We’re voting for you!” she exclaimed, gesturing to her husband. Later, she added, “I like his values.”

Like the mining industry to the east, Minnesota’s timber industry has weathered hard times. The amount of wood harvested declined precipitously during the Great Recession, and has not bounced back, according to government data. Jim Berkeland, 59, a timber buyer for a local paper mill, expressed the kind of economic anxiety that helped Mr. Trump win so solidly here.

“We used to have four paper machines in our mill; now we’re down to one, because of less use of paper,” Mr. Berkeland said, as he watched Mr. Stauber maneuver the rig on a dirt horse-riding ring. “It’s kind of a life of hanging on, and trying to be the last one standing.”

Mr. Berkeland says he votes “the person,” not the party. He came to the expo undecided, but is now a Stauber supporter.

A big part of it, he said, was the fact that the candidate showed up.

Sheryl Gay Stolberg is a congressional correspondent. In 21 years at The Times, she has been a science correspondent, national correspondent, political features reporter and White House correspondent. @SherylNYT

A version of this article appears in print on , on Page A22 of the New York edition with the headline: Courting Other Side And Giving the G.O.P. A Chance to Flip a Seat. Order Reprints | Today’s Paper | Subscribe